How to Convert Angles?

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To convert angles between different units, use the appropriate conversion factors. For example, to convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π.

Angle Conversion Principles

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1. Degrees (°)

The degree is the most common unit for measuring angles. A full circle is 360 degrees.

2. Radians (rad)

The radian is the SI unit for measuring angles. A full circle is 2π radians (approximately 6.28318 radians).

3. Gradians (grad)

The gradian divides a circle into 400 units. A full circle is 400 gradians.

4. Minutes and Seconds

Minutes (′) and seconds (″) are subdivisions of degrees. 1 degree = 60 minutes, 1 minute = 60 seconds.

5. Conversion Formulas

• Degrees to Radians: ° × π/180 = rad
• Radians to Degrees: rad × 180/π = °
• Degrees to Gradians: ° × 400/360 = grad
• Gradians to Degrees: grad × 360/400 = °
• Degrees to Minutes: ° × 60 = ′
• Minutes to Degrees: ′ ÷ 60 = °
• Minutes to Seconds: ′ × 60 = ″
• Seconds to Minutes: ″ ÷ 60 = ′
• Degrees to Turns: ° ÷ 360 = turn
• Turns to Degrees: turn × 360 = °

6. Common Angle Values

• 0° = 0 rad = 0 grad
• 90° = π/2 rad = 100 grad
• 180° = π rad = 200 grad
• 270° = 3π/2 rad = 300 grad
• 360° = 2π rad = 400 grad

Common Angle Units

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Degrees (°)

The most widely used unit for measuring angles. A full circle is 360 degrees.

Radians (rad)

The SI unit for measuring angles. Used extensively in mathematics and physics.

Gradians (grad)

Also called 'gons', used in some surveying and engineering applications.

Minutes (′) and Seconds (″)

Subdivisions of degrees used for precise angle measurements.

Turns and Revolutions

Complete rotations around a circle. 1 turn = 1 revolution = 360° = 2π rad.